Spin-1 lattice-gas model. I. Condensation and solidification of a simple fluid

A spin-1 lattice-gas model, similar to the Blume-Emery-Griffiths model for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures, is shown to describe condensation and solidification of a simple fluid. The Ising-like Hamiltonian of the system involves quadrupolar and dipolar interactions, which are responsible for condensation and solidification, respectively. The molecular-field approximation is used, and the ordinary phase diagram of a simple fluid is reproduced. However, for some range of the parameters, the liquid-gas equilibrium curve disappears. Also, the melting curve may exhibit a tricritical point: For pressures larger than the tricritical pressure, critical melting is found. Other physical applications of the model are briefly discussed.